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Fantom [35]
2 years ago
10

Ms.Kork sold her car for $8,700. This was $100 more than two fifths of what she had paid for the car originally. How much had Ms

.Kork paid for the car?
Mathematics
2 answers:
Eva8 [605]2 years ago
6 0

Answer: 21500

Step-by-step explanation:

marysya [2.9K]2 years ago
3 0

Answer: Ms.Kork paid $21500 for the car.

Step-by-step explanation:

Let x represent the amount of money that Ms.Kork paid for the car.

The amount for which she sold the car was $100 more than two fifths of what she had paid for the car originally. The expression would be

2x/5 + 100

Ms.Kork sold her car for $8,700. It means that

2x/5 + 100 = 8700

2x/5 = 8700 - 100

2x/5 = 8600

Cross multiplying by 5, it becomes

2x = 8600 × 5

2x = 43000

x = 43000/2

x = $21500

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<u>General form of an exponential function</u>

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\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

<h3><u>Asymptote</u></h3>

An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.

The <u>parent function</u> of an <u>exponential function</u> is:

f(x)=b^x

As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

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A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.

A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.

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